I've never seen anyone use Barnes-Hut for an earth gravity model. I'd be curious to see how an implementation like that would work. I think Barnes-Hut is typically used for large N-body simulations where each particle moves independently, like for galactic simulations.
One of the biggest barriers to alternate geopotential models is the availability of trusted data-sets. In another comment someone linked to a PINN based method that looks super promising
One of the biggest barriers to alternate geopotential models is the availability of trusted data-sets. In another comment someone linked to a PINN based method that looks super promising